Negative-Bias Temperature Instability (NBTI), which may lead to performance degradation or even timing failure, has become one of the most drastic challenges in modern multi-core systems. To tolerate NBTI and extend the lifetime of the system, previous researchers proposed maintaining all cores in the multi-core system under similar aging conditions (symmetric aging) through various task assignment algorithms and/or dynamic voltage frequency scaling. Although the concept of symmetric aging provides efficient approaches to tolerating NBTI, it may reduce the lifetime of a multi-core system. If a critical task (i.e., a task with tight timing constraints) arrives when the system has already operated for years, it is possible that none of the equivalently aged cores will be able to complete the critical task within its timing constraints. This unavoidable timing failure then will shorten the lifetime of the system. In contrast, if a few cores are kept robust, these cores can be used to execute the critical task even if all the other cores are aged (asymmetric aging), which avoids timing failure and extends the system lifetime. Based on the above observation, this paper proposes a novel reliability improvement framework that consists of task graph Retiming, task Ordering, task Assignment under asymmetric aging, and Dynamic voltage selection (ROAD) for multi-core systems. With our framework, asymmetric aging can extend the system lifetime through successfully executing critical tasks at the later life stages of the system. The experimental results show that our approach can significantly increase the system lifetime with no or insignificant energy overhead.